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MULTIUSER WIRELESS COMMUNICATION (EE381K) CLASS PROJECT, FALL 20021
Optical CDMA with Optical Orthogonal CodeSANGWOOK HAN
Department of Electrical and Computer Engineering
The University of Texas at AustinAustin, TX 78712
Abstract - This report examines optical CDMA communi-
cation techniques with optical orthogonal codes. Simulationsthat show the desired properties of theses codes and their use
in optical CDMA are reported. Based on the simulations, weinvestigate the properties of optical CDMA. Probability oferror is also evaluated.
I. INTRODUCTION
There have been many efforts to take the full advantageof fiber-optic signal processing techniques to establish an
all optical CDMA communication systems since CDMAwas first applied to the optical domain in the mid-1980s
by Prucnal, Salehi, and others [1-3]. Traditional fiberoptic communication systems use either TDMA or
WDMA schemes to allocate bandwidth among multipleusers. Unfortunately, both present significant drawbacksin local area systems requiring large numbers of users.
In a TDMA system, the total system throughput is
limited by the product of the number of users and theirrespective transmission rates since only one user can
transmit at a time. For instance, if 100 users wish totransmit at 1 gigabit per second, at a minimum the
communication hardware would need to be capable of
sustaining a throughput of 100 gigabits per second, a datarate that would strain even the highest performanceoptical networking equipment. In addition, TDMAsystems show significant latency penalties because of the
coordination required to coordinate and grant requests fortime slots from users by the central node [4].
Unlike TDMA, a WDMA system allows each user totransmit at the peak speed of the network hardware since
each channel is transmitted on a single wavelength oflight. A WDMA system could easily support a bandwidth
of one terabit per second, ideal for the needs of a localarea network. Unfortunately, it is difficult to construct a
WDMA system for a dynamic set of multiple users
because of the significant amount of coordination amongthe nodes required for successful operation. To build a
WDMA network with a dynamic user base, controlchannels and collision detection schemes would need to
be implemented that would waste significant bandwidth.
Fortunately, an alternative to TDMA and WDMA
networking schemes, optical CDMA communicationsystems, require neither the time nor the frequency
management systems. Optical CDMA can operate
asynchronously, without centralized control, and it doesnot suffer from packet collisions. As a result, optical
CDMA systems have lower latencies than TDMA orWDMA. Furthermore, since time and frequency (orwavelength) slots do not need to be allocated to each
individual user, significant performance gains can be
achieved through multiplexing. Also, TDMA andWDMA systems are limited by hardware because of theslot allocation requirements. In contrast, CDMA systems
are only limited the tolerated bit error rate relationship to
the number of users, affording the designer a much moreflexible network design [4].
To establish the optical CDMA, we have to overcome
the code orthogonality problem. Many researchers haveproposed several codes such as prime code, optical
orthogonal code, and so on. In this project, we focus on
optical orthogonal codes (OOC) among those codes. Insection II, we introduce the optical orthogonal codes.
Section III discusses three simulations demonstrating theprinciples of optical CDMA. The first one is for two-user
synchronous channels to understand basics of opticalCDMA and the second one is for two-user asynchronous
channels. The third one is for K-user synchronous
channels. Section IV evaluates the probability of error.
II. OPTICAL ORTHOGONAL CODES
An optical orthogonal code is a family of (0, 1)sequences with good auto- and cross-correlation
properties. Thumbtack-shaped auto-correlation enables
the effective detection of the desired signal (Fig. 2 c), andlow-profiled cross-correlation makes it easy to reduce
interference due to other users and channel noise (Fig. 2d). The use of optical orthogonal codes enables a large
number of asynchronous users to transmit informationefficiently and reliably. The lack of a networksynchronization requirement enhances the flexibility of
the system. The codes considered here consist of truly (0,1) sequences (Fig. 1 a) and are intended for unipolar
environments that have no negative components since youeither have light, or you don't , while most documentedcorrelation sequences are actually (+1, -1) sequences (Fig.1 b) intended for systems having both positive and
negative components.
An (n, w, ?a, ?c) optical orthogonal code C is a familyof (0, 1) sequences of length n and weight w which satisfy
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MULTIUSER WIRELESS COMMUNICATION (EE381K) CLASS PROJECT, FALL 20022
the following two properties [5].
1) The Auto-Correlation Property:
at
n
t
txx
+
=
1
0
(1)
for anyxCand any integer t, 0
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MULTIUSER WIRELESS COMMUNICATION (EE381K) CLASS PROJECT, FALL 20023
Transmitting Part
(a)
(b) (c)
(d) (e)
(f) (g)
(h)
Fig. 3. (a) schematic diagram for a transmitting part (b)signal atA (c) signal atB (d) signal at C(e) signal atD
(f) signal atE(g) signal at F(h) signal at G
On the other hand, if the information bit is 0, no photonpulses are sent in the corresponding frame, i.e., all OFFsignals are sent. In other words, the codeword set is used
as the signature sequence of the transmitter.
Receiving Part
(a)
(b) (c)
(d) (e)
Fig. 4. (a) schematic diagram for a receiving part (b)signal atH(c) signal atI(d) signal atJ(e) signal at K
Basically, optimal CDMA scheme is same as radiofrequency CDMA scheme except using the special codes.Here, we use the matched filter to convert the received
signal in Fig. 3 (h) assuming n(t) in (3) is zero. At the
receiving end, correlation-type decoders are used toseparate the transmitted signals. The decoder consists of abank of 2 tapped delay -lines, one for each codeword. Thedelay taps on a particular line exactly mat ch the signature
sequence, i.e., the delays between successive taps areequal to s2-s1, s3-s2, , optical chips, respectively. Each
tapped delay-line effectively calculates the correlation ofthe received waveform with its signature sequences. InFig. 4 (b) and (c), there are five different correlation
values, 0, 1, 2, 4, and 5. Because of the properties ofoptical orthogonal codes, the correlation between
different signature sequences is low, 0 and 1. Thus thedelay-line output is high, 4 and 5, only when the intended
transmitter s information bit is 1. However, a potential
problem due to interference can be happened. Whencorrelation value has 2, it is definitely due to the
interference. In this case, the value is always below 4 so it
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OPTICAL
H
I
Optical
Decoder
Optical
Decoder
OOC 1
Recovered
Signal
Recovered
Signal++
+
+
OOC 2
G
J
K
Sum
Optical
Encoder
OOC 1
Optical
Encoder
OOC 2
User 1
User 2
C
D
A
B
E
F
G
OPTICAL
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MULTIUSER WIRELESS COMMUNICATION (EE381K) CLASS PROJECT, FALL 20024
can be discarded by choosing relevant threshold value.
But when total number of users goes up, the cross-correlation due to interfering users adds up quickly to
severely degrade the system performance. For instance,
when w is 4 like this case, accommodating 4 users make i tpossible to have 4 as the correlation value even if the
intended transmitter s information bit is 0. To avoid thisphenomenon, both high w which can be considered as the
sum of 1s in the sequence, and long n are required. If weincrease only w fixing n, cross-correlation value due tothe interference can be lowered. However, OOC has very
sparse marks to keep the cross-correlation low, i.e. anumber of zeros is much higher than that of ones in the
sequence. It means that cross-correlation increases byitself by increasing only w. Therefore, both w and nshould be increased simultaneously. But this solution also
reveals a drawback, long signal processing time due tolong n.
Finally the transmitted information is extracted bythresholding the correlator output in Fig. 4 (d) and (e). Inthis case, they are successfully recovered as intended.
Here, 3 is chosen as the threshold values. Threshold issuewill be covered in detail in the section II.2.
II.1.B. Two-User Asynchronous Channel
In optical CDMA, all users are allowed to transmit atany time. There is no network synchronization required.In this section, we simulate a two-user asynchronouschannel to investigate above statement. To verify no
network synchronization, the same scheme in II.I.A. isused here except the time delay at Fin Fig. 3 (a). Fig. 5(b) and (c) show the recovered signals from asynchronousand synchronous channel, respectively. They agree welleven if synchronous channel does not use any special
(a)
(b) (c)Fig. 5. (a) Intended information binary signal (b) recoverd
signal from asynchronous channel (c) recovered signal
from synchronous channel
scheme for synchronization. Therefore, now we can say
that optical CDMA does need no network synchronization.
II.2. K-User Synchronous Channel
In the previous section, we investigated a simple 2-user
channel to understand the optical CDMA. In this section,we explore problems faced by increasing K (Fig. 6 a).
Here we choose 7 as K, and Cis (43, 3, 1, 1) having 7 sets,{{0, 1, 19}, {0, 2, 22}, {0, 3, 15}, {0, 4, 13}, {0, 5, 16},{0, 6, 14}, {0, 7, 17}}.
The first issue is a threshold value. As we saw in the
previous section, interfering signal can be effectivelydiscarded by setting a relevant threshold value. Thethreshold value can be chosen under the following
condition.wthreshold0 (4)
Fig. 6 (d) through (g) show results from several threshold
values, 1, 2, 3, and 5. As the threshold value goes up, therecovered signal gets similar to the ideal signal in Fig. 6(c). However, the threshold value can not be over w. If theintended information bit is 1, the correlation value is w.
Therefore, the threshold over w incorrectly converts it to
0 when the intended information bit is 1. Fig. 6 (g) showsthe results by choosing threshold over w. We can clearlysee that a dotted line is missed comparing to Fig. 6 (c).
Even if the highest value under (4) is chosen (Fig. 6 f),the recovered signal can not be exactly same as the ideal
pattern. In the Fig. 6 (a), if the intended information bit is1, the correlation value is w(=3). But a s we alreadydiscussed in the previous section, the cross-correlation
due to interfering users adds up very quickly to severelydegrade the system performance. Here, the correlationvalue due to interference is even higher than w(=3). Thisis the reason why the received signal can not be recovered
perfectly.
To figure it out above problem we introduce opticalhard-limiter [3] located before the optical tapped-delayline (Fig. 7 a). An ideal optical hard- limiter is defined as
10
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,1)(
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MULTIUSER WIRELESS COMMUNICATION (EE381K) CLASS PROJECT, FALL 20025
(a)
(b) (c)
(d) (e)
(f) (g)
Fig. 6 (a) schematic diagram of a receiving part for Kusers (b) signal at H (c) ideal signal at J(d) signal at J
when threshold=1 (e) signal at Jwhen threshold=2 (f)signal at J when threshold=3 (g) signal at J whenthreshold=5
All optical light intensity which is bigger than or equal
to one are clipped back to one in Fig. 7 (d). In Fig 7 (f),the cross-correlation value over w due to the interference
does not exist any more. From these, the thresolding can
much effectively recover the information. Fig. 7 (g) and(h) show the recovered signals without and with the
optical hard-limiter, respectively. We can clearly see thatFig. 7 (h) is much similar to the intended signal (Fig. 7 i).
Consequently, we can say that the optical hard-limiter caneffectively lower the interference effect.
(a)
(b)
(c) (d)
(e) (f)
(g) (h)
(i)
Fig. 7. (a) receiving part wit hout optical hard-limiter (b)receiving part with optical hard-limiter (c) signal at G
(d) signal at G (e) signal atH(f) signal atH (g) signalatJ(h) signal atJ (i) ideal signal expected atJ
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H J
Optical
Decoder
OOC 1
Recovered
Signal+ +
Optical
Decoder
OOC K
Recovered
Signal+ +
G
Optical
Decoder
OOC
Recovered
Signal++
JHG ?
Optical
Decoder
OOC
Recovere
Signal++
Hard
Limiter JHG
?
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MULTIUSER WIRELESS COMMUNICATION (EE381K) CLASS PROJECT, FALL 20026
IV. PROBABILITY OF ERROR
The probability of error per bit is defined as
PE=p(LIth | b=0)?p(b=0)
+p(LI